Question

Find the average value of the function on the given interval
f(x) = sin4x, [-Ï€,Ï€]

Answer 1

\[\frac{1}{2\pi}\int_{-\pi}^{\pi}\sin(4x)dx\]

Answer 2

since sine is odd, this should be zero, but it is easy enough to check as the anti derivative of \(\sin(4x)\) is \(-\frac{1}{4}\cos(4x)\)